A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag

International Journal for Numerical and Analytical Methods in Geomechanics

Volumn 35, Issue 5, 2011, Pages 602-629

  Gordeliy, E ^a   Detournay, E ^a,b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b CSIRO   (Australia)

Author keywords

Fracture mechanics; Hydraulic fracture; Level set

Indexed keywords

ALGEBRAIC EQUATIONS; AXISYMMETRIC CONDITIONS; CONSTANT-STEP; CPU TIME; DISPLACEMENT DISCONTINUITY METHOD; ELASTICITY EQUATIONS; FILLING FRACTIONS; FIXED GRID ALGORITHM; FIXED GRIDS; FIXED POINT ITERATION; FLUID FRONTS; FLUID VELOCITIES; FLUID VOLUMES; FREE SURFACES; FRONT TRACKING; HYDRAULIC FRACTURE; LEVEL SET; LEVEL SET ALGORITHM; LOW STRESS; LUBRICATION EQUATION; MATCHING LOCATION; NEWTON'S METHODS; ORDERS OF MAGNITUDE; PLANE STRAINS;

ALGEBRA; ALGORITHMS; ELASTICITY; FINITE VOLUME METHOD; FLUIDS; FRACTURE MECHANICS; HYDRAULIC FRACTURING; HYDRAULICS; LINEAR SYSTEMS; NEWTON-RAPHSON METHOD; NONLINEAR SYSTEMS; NUMERICAL METHODS; TIME VARYING SYSTEMS;

FRACTURE;

ALGORITHM; FINITE VOLUME METHOD; FRACTURE MECHANICS; HYDRAULIC FRACTURE; NONLINEARITY; NUMERICAL MODEL; PLANE STRAIN;

EID: 78751551341     PISSN: 03639061     EISSN: 10969853     Source Type: Journal    
DOI: 10.1002/nag.913     Document Type: Article

References (53)

1. Khristianovic SA, Zheltov YP. Formation of vertical fractures by means of highly viscous fluids. Proceedings of the 4th World Petroleum Congress, Rome, Vol. II, 1955; 579-586.
2. Adachi JI, Siebrits E, Peirce AP, Desroches J. Computer simulation of hydraulic fractures. International Journal of Rock Mechanics and Mining Science 2007; 44(5):739-757.
3. Murdoch LC, Slack WW. Forms of hydraulic fractures in shallow fine-grained formations. Journal of Geotechnical and Geoenvironmental Engineering 2002; 128(6):479-487.
4. Murdoch LC. Mechanical analysis of idealized shallow hydraulic fracture. Journal of Geotechnical and Geoenvironmental Engineering 2002; 128(6):488-495.
5. Young C. Controlled-foam injection for hard rock excavation. In Rock Mechanics for Industry, Proceedings of 37th U.S. Rock Mechanics Symposium, Vail, Colorado, vol. 1. Rotterdam: Balkema, 1999; 115-122.
6. Jeffrey RG, Mills KW. Hydraulic fracturing applied to inducing longwall coal mine goaf falls. Pacific Rocks 2000. Rotterdam: Balkema, 2000; 423-430.
7. van As A, Jeffrey RG. Caving induced by hydraulic fracturing at Northparkes mines. Pacific Rocks 2000. Rotterdam: Balkema, 2000; 353-360.
8. Abou-Sayed AS, Andrews DE, Buhidma IM. Evaluation of oily waste injection below the permafrost in Prudhoe Bay field. Proceedings of the California Regional Meetings, Bakersfield, CA. Society of Petroleum Engineers: Richardson, TX, 1989; 129-142.
9. Abou-Sayed AS, Thompson TW, Keckler K. Safe injection pressures for disposing of liquid wastes: a case study for deep well injection (SPE/ISRM-28236). Proceedings of the Second SPE/ISRM Rock Mechanics in Petroleum Engineering, Balkema, 1994; 769-776.
10. Bolzon G, Cochetti G. Direct assessment of structural resistance against pressurized fracture. International Journal for Numerical and Analytical Methods in Geomechanics 2003; 27:353-378.
11. Penman ADM. The failure of the Teton dam. Ground Engineering 1977; 10(6):18-27.
12. Pollard DD, Johnson AM. Mechanics of growth of some laccolithic intrusions in the Henry Mountains, Utah. II. Tectonophysics 1973; 18:311-354.
13. Pollard DD, Hozlhausen G. On the mechanical interaction between a fluid-filled fracture and the earth's surface. Tectonophysics 1979; 53:27-57.
14. Corry CE. Laccoliths: Mechanics of Emplacement and Growth, Special Publications. Geological Society of America, 1988.
15. Fialko Y. On origin of near-axis volcanism and faulting at fast spreading mid-ocean ridges. Earth and Planetary Science Letters 2001; 190:31-39.
16. Zhang X, Detournay E, Jeffrey R. Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space. International Journal of Fracture 2002; 115:125-158.
17. Bunger AP. Near-surface hydraulic fracture. Ph.D. Thesis, University of Minnesota, July 2005.
18. Zhang X, Jeffrey RG, Detournay E. Propagation of a hydraulic fracture parallel to a free surface. International Journal for Numerical and Analytical Methods in Geomechanics 2005; 29(13):1317-1340.
19. Roper SM, Lister JR. Buoyancy-driven crack propagation from an over-pressured source. Journal of Fluid Mechanics 2005; 536:79-98.
20. Roper SM, Lister JR. Buoyancy-driven crack propagation: the limit of large fracture toughness. Journal of Fluid Mechanics 2007; 580:359-380.
21. Medlin WL, Masse L. Laboratory experiments in fracture propagation. Society of Petroleum Engineers Journal 1984; 256-268.
22. Rubin AM. Propagation of magma-filled cracks. Annual Review of Earth and Planetary Sciences 1995; 23:287-336.
23. Bunger AP, Jeffrey RG, Detournay E. Toughness-dominated near-surface hydraulic fracture experiments. In GulfRock04 Conference, Yale DP, Willson SM, Abou-Sayed AS (eds), Houston, ARMA, 2004.
24. Sher EN, Mikhailov AM. Modeling the axially symmetric crack growth under blasting and hydrofracturing near free surface. Journal of Mining Science 2008; 44(5):473-481.
25. Paynter RJH, Hills DA, Sackfield A. The penny crack beneath the surface of a half-space: with application to the blister test. International Journal of Fracture 2006; 142:173-182.
26. Garagash DI, Detournay E. The tip region of a fluid-driven fracture in an elastic medium. ASME Journal of Applied Mechanics 2000; 67(1):183-192.
27. Garagash DI. Propagation of a plane-strain hydraulic fracture with a fluid lag: Early-time solution. International Journal of Solids and Structures 2006; 43:5811-5835.
28. Bunger AP, Detournay E. Early time solution for a penny-shaped hydraulic fracture. ASCE Journal of Engineering Mechanics 2007; 133(5):534-540.
29. Detournay E, Bunger AP. Similarity solutions for a shallow hydraulic fracture. In Eurock 2006: Multiphysics Coupling and Long Term Behaviour in Rock Mechanics, Cotthem AV, Charlier R, Thimus J-F, Tshibangu J-P (eds), 2006; 57-62. ISBN: 0-415-41001-0, ISRM.
30. Peirce AP, Detournay E. An implicit level set method for modeling hydraulically driven fractures. Computer Methods in Applied Mechanics and Engineering 2008; 197:2858-2885.
31. Bunger AP, Detournay E. Experimental validation of the tip asymptotics for a fluid-driven crack. Journal of the Mechanics and Physics of Solids 2008; 56(11):3101-3115.
32. Garagash DI, Detournay E, Adachi JI. Multiscale tip asymptotics for fluid-driven fracture. Journal of Fluid Mechanics 2010; submitted.
33. Lecampion B, Detournay E. An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag. Computer Methods in Applied Mechanics and Engineering 2007; 196(49-52):4863-4880.
34. Sethian JA. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press: Cambridge, U.K., 1999.
35. Crouch SL, Starfield AM. Boundary Element Methods in Solid Mechanics. George Allen and Unwin: London, 1983.
36. Hills DA, Kelly PA, Dai DN, Korsunsky AM. Solution of Crack Problems. The Distributed Dislocation Technique. Solid Mechanics and its Applications, vol. 44. Kluwer Academic Publishers: Dordrecht, 1996.
37. Johnson AM. Physical Processes in Geology. Freeman, Cooper and Company: San Francisco, 1970.
38. Dyskin AV, Germanovich LN, Ustinov KB. Asymptotic analysis of crack interaction with free boundary. International Journal of Solids and Structures 2000; 37(6):857-886.
39. Bunger AP, Detournay E. Asymptotic solution for a penny-shaped near-surface hydraulic fracture. Engineering Fracture Mechanics 2005; 72(16):2468-2486.
40. Batchelor GK. An Introduction to Fluid Dynamics. Cambridge University Press: Cambridge, U.K., 1967.
41. Detournay E. Propagation regimes of fluid-driven fractures in impermeable rocks. International Journal of Geomechanics 2004; 4(1):1-11.
42. Lin CC, Segel LA. Mathematics Applied to Deterministic Problems in the Natural Sciences. SIAM: Philadelphia, 1988.
43. Peirce AP, Siebrits E. A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems. International Journal for Numerical Methods in Engineering 2005; 63:1797-1823.
44. Peirce AP. Localized Jacobian ILU preconditioners for hydraulic fractures. International Journal for Numerical Methods in Engineering 2006; 65(12):1935-1946.
45. Ryder JA, Napier JAL. Error analysis and design of a large-scale tabular mining stress analyzer. Proceedings of the 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1985; 1549-1555.
46. Sethian JA. Fast marching methods. SIAM Review 1999; 41(2):199-235.
47. Gordeliy E, Detournay E. Oribi: implicit fixed grid algorithm to simulate propagation of shallow hydraulic fractures. 2010. Available at .
48. Paynter RJH, Hills DA, Korsunsky AM. The effect of path cut on Somigliana ring dislocation elastic fields. International Journal of Solids and Structures 2007; 44:6653-6677.
49. Paynter RJH, Hills DA. The effect of path cut on Somigliana ring dislocations in a half-space. International Journal of Solids and Structures 2009; 46:412-432.
50. Korsunsky AM. The Somigliana ring dislocation revisited. 1. Papkovich potential solutions for dislocations in an infinite space. Journal of Elasticity 1996; 44(2):97-114.
51. Korsunsky AM. The Somigliana ring dislocation revisited. 2. Solutions for dislocations in a half space and in one of two perfectly bonded dissimilar half spaces. Journal of Elasticity 1996; 44(2):115-129.
52. Kolesnikova AL, Romanov AE. Dislocation and disclination loops in the virtual-defect method. Physics of the Solid State 2003; 45(9):1706-1718.
53. Kolesnikova AL, Romanov AE. Virtual circular dislocation-disclination loop technique in boundary value problems in the theory of defects. Journal of Applied Mechanics 2004; 71(3):409-417.